Related papers: Tailoring Reproducing Kernels for Optimal Control …

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

Actor-critic (AC) methods are a cornerstone of reinforcement learning (RL) but offer limited interpretability. Current explainable RL methods seldom use state attributions to assist training. Rather, they treat all state features equally,…

This paper derives error bounds for regression in continuous time over subsets of certain types of Riemannian manifolds.The regression problem is typically driven by a nonlinear evolution law taking values on the manifold, and it is cast as…

We propose a new, nonparametric approach to learning and representing transition dynamics in Markov decision processes (MDPs), which can be combined easily with dynamic programming methods for policy optimisation and value estimation. This…

We develop a non-parametric, data-driven, tractable approach for solving multistage stochastic optimization problems in which decisions do not affect the uncertainty. The proposed framework represents the decision variables as elements of a…

Estimating Kullback Leibler (KL) divergence from samples of two distributions is essential in many machine learning problems. Variational methods using neural network discriminator have been proposed to achieve this task in a scalable…

Estimating the dissipativity of nonlinear systems from empirical data is useful for the analysis and control of nonlinear systems, especially when an accurate model is unavailable. Based on a Koopman operator model of the nonlinear system…

We propose a new decentralized robust kernel-based learning algorithm within the framework of reproducing kernel Hilbert spaces (RKHSs) by utilizing a networked system that can be represented as a connected graph. The robust loss function…

Actor-critic (AC) algorithms are known for their efficacy and high performance in solving reinforcement learning problems, but they also suffer from low sampling efficiency. An AC based policy optimization process is iterative and needs to…

Selecting an appropriate kernel is a central challenge in kernel-based spectral methods. In \emph{Kernelized Diffusion Maps} (KDM), the kernel determines the accuracy of the RKHS estimator of a diffusion-type operator and hence the quality…

The reproducing kernel Hilbert space (RKHS) embedding of distributions offers a general and flexible framework for testing problems in arbitrary domains and has attracted considerable amount of attention in recent years. To gain insights…

We develop a mathematical framework to address a broad class of metric and preference learning problems within a Hilbert space. We obtain a novel representer theorem for the simultaneous task of metric and preference learning. Our key…

In $\mathbb R^d$, it is well-known that cumulants provide an alternative to moments that can achieve the same goals with numerous benefits such as lower variance estimators. In this paper we extend cumulants to reproducing kernel Hilbert…

Reproducing kernel Hilbert spaces are elucidated without assuming prior familiarity with Hilbert spaces. Compared with extant pedagogic material, greater care is placed on motivating the definition of reproducing kernel Hilbert spaces and…

Any applied mathematical model contains parameters. The paper proposes to use kernel learning for the parametric analysis of the model. The approach consists in setting a distribution on the parameter space, obtaining a finite training…

Kernel based methods have shown effective performance in many remote sensing classification tasks. However their performance significantly depend on its hyper-parameters. The conventional technique to estimate the parameter comes with high…

Policy iteration (PI) is a widely used algorithm for synthesizing optimal feedback control policies across many engineering and scientific applications. When PI is deployed on infinite-horizon, nonlinear, autonomous optimal-control…

We propose and discuss a new computational method for the numerical approximation of reachable sets for nonlinear control systems. It is based on the support vector machine algorithm and represents the set approximation as a sublevel set of…

Kernel-based methods offer a powerful and flexible mathematical framework for addressing histopolation problems. In histopolation, the available input data does not consist of pointwise function samples but of averages taken over intervals…

The linear quadratic regulator problem is central in optimal control and was investigated since the very beginning of control theory. Nevertheless, when it includes affine state constraints, it remains very challenging from the classical…